Remark 4.8 Under linear MDP assumption, this regret bound is at the same order as the LSVI-UCB algorithm from [1]} and \(\sqrt{dH}\)  better than the state-of-the-art TS-type algorithm [2]}. The only work that enjoys a \(\sqrt{d}\)  better regret is [3]}, which requires solving an intractable optimization problem.

